Monthly Archives: June 2019

183: the towel riddle

I was showering one day when I was hit with a paranoid thought. Said thought put down roots and blossomed into a full-blown riddle. When I told it to my DnD circle, they viciously put it through the wringer and helped me refine it quite a bit.

The riddle

After your workout, you go to the locker room for a shower. Your gym is generous and provides free towel service, so nobody who comes to this gym brings their own towel. Instead, there’s a common pile of towels for anyone to grab in the locker room. Common courtesy dictates that

  1. Towels have no owner until touched by a user.
  2. Once touched and taken from the pile, a towel logically belongs to the touchee and should be considered theirs.
  3. Towel users relinquish ownership of their towels by depositing them in the return bin (to be cleaned etc. etc.).
  4. Ownership is not transferable – touching an owned towel makes you a thief.

You grab a towel from the pile. This towel is now yours since you have touched it and removed it from the communal pile. You enter the shower, hanging up your towel on the peg just outside your stall. You shower up and finish. You reach for the peg, ready to dry off, but the person in the neighboring stall interrupts you.

“I’m sorry,” he or she ventures, “that’s my towel.”

“There must be some mistake,” you reply. “I definitely left my towel on this peg.”

The important meta-facts

The riddle-teller digresses here to lay down some truths not directly presented by the story.

  1. Neither you nor your neighbor are lying. Both of you are telling the truth in good faith. Neither of you is actively attempting to deceive the other.
  2. Neither you nor your neighbor are thieves, nor do either of you intend to become such.

The less important meta-facts

Here are some silly facts that try to pre-empt the more outlandish answers. (Hopefully they don’t just distract the riddle-hearer.)

  1. The towel pile cannot be annexed all at once – i.e. you cannot move the whole pile a centimeter and claim them all. Assume that nobody takes more than one towel from the pile per try to the gym.
  2. Leaving the gym trivially releases your ownership over any towels you’ve taken. Removing them from the gym makes you a thief, but assume nobody does that. Also, nobody lives at the gym to slowly take all the towels.
  3. The exact dimensions and number of shower stalls is mostly irrelevant – however, it may help to imagine both you and your neighbor as not having wall-side stalls.
  4. There is no intentional wordplay above. Only the dialogue between your neighbor and you has significance embedded in the wording, but it can still be rephrased validly in many ways.

The answer

My answer was that as you stepped in the shower, you hung your towel on the peg between you and your neighbor. However, your honest neighbor wasn’t there just yet – some other person (let’s call him or her Taylor) was showering in the adjoining stall. Taylor hopped into the shower, hanging his or her towel in line with your convention (depending if Taylor is on your right or your left – anyhow, Taylor hung his or her towel a whole stall away from you). However, once Taylor finished showering, Taylor mistakenly took your towel by mistake and went away.

At this point, your honest neighbor hopped into Taylor’s old stall. Seeing a towel hung up on the far peg, he or she chooses to hang his or her towel on the peg where your towel formerly hung. Therefore the towel is in fact your neighbor’s, and you did indeed leave your towel on that same peg. Unfortunately, you were inadvertently about to make a thief of yourself (but the dialogue stops just short of that).

Someone ventured a better answer, actually, which requires far less explaining: your towel fell off the peg just before your honest neighbor stepped into the adjoining stall. The same result applies.